$A$ body of mass $0.5\; kg$ travels in a straight line with velocity $v=a x^{3/2}$ where $a=5\; m^{-1/2} s^{-1}$. What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m$?

$A$ toy gun fires a plastic pellet with a mass of $0.5\ g$. The pellet is propelled by a spring with a spring constant of $1.25\ N/cm$, which is compressed $2.0\ cm$ before firing. The plastic pellet travels horizontally $10\ cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\ N$. What is the speed (in $SI\ units$) of the bullet as it emerges from the barrel?

An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

$A$ body of mass $m$ is travelling with a velocity $u$. When a constant retarding force $F$ is applied,it comes to rest after travelling a distance $s_{1}$. If the initial velocity is $2u$,with the same force $F$,the distance travelled before it comes to rest is $s_{2}$. Then,

$A$ particle is released from height $S$ above the surface of the earth. At a certain height,its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively:

$A$ pendulum bob on a $2\, m$ string is displaced $60^\circ$ from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path? (Take $g = 9.8\, m/s^2$)